| Summary: | Dementia, a stepwise deterioration of cognitive function, affects over 700,000 people in the UK, resulting in over 60,000 deaths and a cost of over £1.7 billion each year. It is believed to have a combination of vascular and degenerative origins and to have correlations with localised lesions, or infarctions, in the brains of affected patients. Mini-strokes are one of the causes for this disease as the presence of ischemia is highly related to the risk factors for dysfunction of the neurovascular unit. The underlying interacting mechanisms are, however, often very complex and they remain largely poorly understood. The cerebral microvascular bed is highly irregular and localised variations in its structure are large. To capture these variations, statistical algorithms are required, rather than large volumes of expensive experimental data. Therefore, accurate modelling of blood flow and oxygen transport at the microvascular level is important in improving our understanding of the structure and function of the cerebral vasculature and hence of brain diseases. A novel algorithm is proposed here to create artificial microvascular networks that match quantitatively experimental data previously obtained in human brain tissue. Blood flow and oxygen transport in the network and the tissue are analysed through both discretised and continuum transport models. By disabling flow sources, ischemic events can be simulated. Using multiple networks, the influence of individual network structures on the response to ischemia is analysed. The relationship between the discretised and continuum formulations of the model is quantified, providing a means for scaling up the model over multi length scales. Finally, the phenomenon of microvessel collapse under ischemic conditions is examined and it is shown that this is fundamentally dependent upon the variability found at the network level, since it cannot be modelled by a continuum model. An initial infarction is also found to facilitate the occurrence of collapse events for most networks.
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